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中文摘要：
关于多项式函数算法优化问题，人工神经网络是解决函数逼近问题的一个重要方法。但由于传统的学习型神经网络存在缺陷，如对初始权重非常敏感，极易收敛于局部极小；收敛缓慢甚至不能收敛；过拟合与过训练；网络隐含节点数不确定等。针对上述问题，提出了一种多项式函数的三层泛函网络与逼近算法，并给出了中间隐层计算单元个数是如何确定。提出的算法能以任意精度逼近多项式函数，同时具有较快收敛速度和良好性能，克服了人工神经网络的不足。最后，给出了两个数值算例进一步验证算法的正确性。
英文摘要：
Artificial neural network is to solve the function approximation problem and is an important method, but due to the defects of traditional learning neural network, such as sensitive initial weights, local minimum, slow convergence speed, over fitting and training, and uncertainty of network hidden nodes. Aiming at these problems, the paper put forward a polynomial function of three layer functional network and approximation algorithm, and gave the determining method of hidden layer calculation unit number. The algorithm can approximate arbitrary precision of the polynomial function, and has fast convergence speed and good performance. Finally, two numerical examples were given to further validate the calculation results.
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